Copiaco , Chile -LRB- CNN -RRB- -- The wife of one of the 33 men trapped 2,300 feet below ground in Chile gave birth Tuesday to a daughter , a relative said .

Elizabeth Segovia , wife of Ariel Ticona , was recovering in a hospital after giving birth to a 4-kilogram -LRB- 8.8 lbs . -RRB- , 48-centimeter -LRB- 19-inch -RRB- girl , said Ticona 's sister , Veronica Ticona .

The daughter was to have been named Carolina , but that plan was changed after the August 5 cave-in trapped her father , Veronica Ticona said .

Nearly two weeks ago , Segovia got a handwritten letter from her husband -- sent through the 4-inch-wide hole that has served as an umbilical cord to the miners -- proposing they name their daughter Esperanza Elizabeth instead . Esperanza is Spanish for hope .

`` First , because we never lost hope ; second , because it 's the name of the camp where the families are living ; and third , because the 33 miners never lost hope either , '' Segovia said earlier in September .

Esperanza is believed to be the first child born to any of the 33 men since they were trapped .

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In the 40 days that have followed , their contact with the outside world has been limited to what rescuers have been able to pass through the narrow hole that reaches into the cave ceiling .

Ticona said her brother was told of the birth by a video conference system . `` He is very happy to be a father , '' she said .

Segovia discovered that their child would be a girl by looking at a grainy ultrasound on August 4 , the day before the mine collapse . `` My world just collapsed , '' she said earlier this month . `` I could n't react . I just cried and cried . ''

But , she added , she forced herself to stop crying because doing so adversely affected her fetus .

The tube to the mine has carried life-affirming news in both directions . A few days after seeing her daughter on grainy , flickering ultrasound images , Segovia saw her husband on grainy video that the miners shot by the flickering lights mounted on their mining helmets , then packed into the tube for the journey upward .

With her daughter 's arrival Tuesday , Segovia is now waiting for her husband 's arrival in the months ahead .

The couple also have two sons , ages 5 and 9 .

CNN 's Karl Penhaul contributed to this story .

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Daughter was to have been named Carolina , but plan changed after cave-in

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Miners have been trapped 40 days

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Segovia discovers a day before mine collapse that girl was expected

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Days later she saw her husband on a video the miners shot